Question

select the quantum numbers associated with the 5d orbital.
principal quantum number (n)
□,□,...
angular momentum quantum number (l)
□
possible magnetic quantum numbers (m_l)
□

Explanation:

Step1: Determine principal quantum number (\(n\))

The orbital is \(5d\). The principal quantum number \(n\) is the number in the orbital notation (the coefficient). So for \(5d\), \(n = 5\).

Step2: Determine angular momentum quantum number (\(l\))

The angular momentum quantum number \(l\) is determined by the subshell. For \(s\) subshell, \(l = 0\); \(p\) subshell, \(l = 1\); \(d\) subshell, \(l = 2\); \(f\) subshell, \(l = 3\). Since it's a \(d\) orbital, \(l = 2\).

Step3: Determine magnetic quantum numbers (\(m_l\))

The magnetic quantum number \(m_l\) ranges from \(-l\) to \(+l\) including zero. For \(l = 2\), \(m_l\) can be \(-2, -1, 0, +1, +2\).

Answer:

• Principal quantum number (\(n\)): \(5\)
• Angular momentum quantum number (\(l\)): \(2\)
• Possible magnetic quantum numbers (\(m_l\)): \(-2, -1, 0, +1, +2\)